Agree on nixing the mesh gear. Sounds to me like you were in a boil bag!

No, absolutely not. There is always air coming in through sleeve openings, collar, zippers and even the general fabric (as long as you don't use anything with a membrane). That is enough to cool you down through evaporation of the water you soaked a shirt with.

Give it a try: use a long sleeve shirt under a jacket, put water on one arm so that it's soaked but not dripping and go ride in the heat. As long as you're moving this arm will be cool, nearly cold. Do that in some strategic places (chest, arms, helmet cap, neck tube, thighs) and you stay very comfortable - only requirement is a little bit of airflow. Don't open too many or too large vents, as the water will evaporate too quickly.

I soaked my stuff in Furnace Creek inside Death Valley and was comfortable until Independence. Soaked my stuff again there and was good until we reached Yosemite where I was significantly cooler anyways.